Average Error: 0.0 → 0.0
Time: 9.0s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\left(\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \left|\sqrt[3]{\frac{\sinh y}{y}}\right|\right)\right) \cdot \sqrt{\sqrt[3]{\sqrt{\frac{\sinh y}{y}}}}\right) \cdot \sqrt{\sqrt[3]{\sqrt{\frac{\sinh y}{y}}}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\left(\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \left|\sqrt[3]{\frac{\sinh y}{y}}\right|\right)\right) \cdot \sqrt{\sqrt[3]{\sqrt{\frac{\sinh y}{y}}}}\right) \cdot \sqrt{\sqrt[3]{\sqrt{\frac{\sinh y}{y}}}}
double f(double x, double y) {
        double r133114 = x;
        double r133115 = cos(r133114);
        double r133116 = y;
        double r133117 = sinh(r133116);
        double r133118 = r133117 / r133116;
        double r133119 = r133115 * r133118;
        return r133119;
}
↓
double f(double x, double y) {
        double r133120 = x;
        double r133121 = cos(r133120);
        double r133122 = y;
        double r133123 = sinh(r133122);
        double r133124 = r133123 / r133122;
        double r133125 = sqrt(r133124);
        double r133126 = cbrt(r133124);
        double r133127 = fabs(r133126);
        double r133128 = r133125 * r133127;
        double r133129 = r133121 * r133128;
        double r133130 = cbrt(r133125);
        double r133131 = sqrt(r133130);
        double r133132 = r133129 * r133131;
        double r133133 = r133132 * r133131;
        return r133133;
}

Error

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Results

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Derivation

  1. Initial program 0.0

    \[\cos x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \cos x \cdot \color{blue}{\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right)}\]

  4. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.0

    \[\leadsto \left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\color{blue}{\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}}}\]

  7. Applied sqrt-prod0.0

    \[\leadsto \left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \color{blue}{\left(\sqrt{\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}} \cdot \sqrt{\sqrt[3]{\frac{\sinh y}{y}}}\right)}\]

  8. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(\left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\sqrt[3]{\frac{\sinh y}{y}}}}\]

  9. Simplified0.0

    \[\leadsto \color{blue}{\left(\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \left|\sqrt[3]{\frac{\sinh y}{y}}\right|\right)\right)} \cdot \sqrt{\sqrt[3]{\frac{\sinh y}{y}}}\]
  10. Using strategy rm

  11. Applied add-sqr-sqrt0.0

    \[\leadsto \left(\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \left|\sqrt[3]{\frac{\sinh y}{y}}\right|\right)\right) \cdot \sqrt{\sqrt[3]{\color{blue}{\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}}}}\]

  12. Applied cbrt-prod0.0

    \[\leadsto \left(\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \left|\sqrt[3]{\frac{\sinh y}{y}}\right|\right)\right) \cdot \sqrt{\color{blue}{\sqrt[3]{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}}}\]

  13. Applied sqrt-prod0.0

    \[\leadsto \left(\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \left|\sqrt[3]{\frac{\sinh y}{y}}\right|\right)\right) \cdot \color{blue}{\left(\sqrt{\sqrt[3]{\sqrt{\frac{\sinh y}{y}}}} \cdot \sqrt{\sqrt[3]{\sqrt{\frac{\sinh y}{y}}}}\right)}\]

  14. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(\left(\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \left|\sqrt[3]{\frac{\sinh y}{y}}\right|\right)\right) \cdot \sqrt{\sqrt[3]{\sqrt{\frac{\sinh y}{y}}}}\right) \cdot \sqrt{\sqrt[3]{\sqrt{\frac{\sinh y}{y}}}}}\]

  15. Final simplification0.0

    \[\leadsto \left(\left(\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \left|\sqrt[3]{\frac{\sinh y}{y}}\right|\right)\right) \cdot \sqrt{\sqrt[3]{\sqrt{\frac{\sinh y}{y}}}}\right) \cdot \sqrt{\sqrt[3]{\sqrt{\frac{\sinh y}{y}}}}\]

Reproduce

herbie shell --seed 2019362 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))